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Electret model used in TIDU765 design

CRC39681
Prodigy 20 points
Other Parts Discussed in Thread: LM6171, TL081, OPA322

Greetings everyone,

I am going through the TIDU765 design (John Caldwell) in an attempt to grasp the details of the Eletret microphone.

This article is great work being clear and precise. However, there is one point that I do not understand. At pg. 11 a "basic model" is used to simulate the circuit. My problem is the output impedance of 2.2Kohm specified for the modeled electret (see pg. 5, table 2 same article).

I do not see this output impedance explicitly captured by the model ...

My hypothesis is that, because of the usage of the electret in the rest of the pre-amplifier circuit the output impedance does not matter  ... but I would like a second opinion.

Thanks!

Cristian

  • 0
    TI__Genius 12325 points

    Hi Cristian,

    Thank you for your question. The "impedance" specified in the microphone datasheet, and consequently on page 5 of my article is an external bias resistor connected to the microphone when the other parameters are measured. For AC signals, the output impedance of the capsule is in parallel with the bias resistor. For simplicity, I chose to model the capsule as having essentially an infinite output impedance (ideal current source), and therefore the output impedance of the capsule and bias resistor combination is determined entirely by the bias resistor. In reality, the output impedance of the capsule is of course finite but often not specified in microphone datasheets. The output impedance is determined entirely by the internal JFET of the capsule, (which is usually selected on the basis of cost and low gate leakage rather than ultra high output impedance; a function of the JFET's channel length modulation) and the drain current that the JFET is biased at. It would be very nice if microphone datasheets included this type of information, but unfortunately most do not. 

  • 0 in reply to John Caldwell
    Prodigy 20 points

    Hi John,

    Thank you so much for taking your time to answer my question. For the sake of understanding I would like to address a subsequent one.

    I believe that the output impedance of a typical EMC (the one given by the JFET, let's call it Zo) is in the order of a few 1000 ohms.The (external) resistor that you used in equation (4) is 2.2K -- because for the small-signal-model and considering Zo infinite or very large.

    Could it be that the 2.2K in equation (4) is the "actual" external resistor used in the sensibility measurement in parallel with the actual Zo (which is actually a few Kohms)?

    Would you please care to correct or validate this?

    Gratefully,

    Cristian

  • 0 in reply to CRC39681
    TI__Genius 12325 points

    Well 2.2k is a fairly standard value for an external resistor connected to electret microphones so I'm reasonably confident that the sensitivity of the microphone was measured with a 2.2k resistor connected. You're probably correct on the output impedance of the internal JFET only being a few kilo-ohms (and this will also likely be dependent on the drain current the microphone is biased at) so I think the "actual" output impedance of the bias resistor and microphone combination is closer to 2.2k in parallel with ~3k which is 1.27k Ohms. It might be better to reach out to a microphone company to see if they can comment on this?

  • 0 in reply to John Caldwell
    Prodigy 10 points

    John,

    I was intrigued by your reference circuit for an electret microphone preamp.

    I just saw it recently, after classes were over this past spring semester here at UT Austin.

    One of the labs in Analog Electronics that I teach was a high-gain electret mic preamp (using conventional non-inverting and inverting op amp connections.

    The promising and intriguing aspects of the transimpedance configuration were:

    1. the nose reduction by eliminating the input resistor

    2. the use of a single supply op amp without having to resort to very small input offset voltage due to the high gain (say up to 40 dB for a voltage amplifier connection).

    However, I think I can shed some light on the microphone source impedance question, and it results in a caution and condition that the op amp used needs extra bandwidth in order to avoid limiting the total BW to less than 10 kHz.

    In just a few words, the issue is the following:

    The microphone’s JFET is operated with zero gate bias (and a very small AC input voltage).  So I modeled it as a source (Thevenin or Norton) and did a brute force simulation to find its output resistance (see figure).  I capacitively coupled it to a load resistance, R1, and reduced the resistance from a large value (where the open-circuit voltage is found) to a value where the output AC voltage was 1/2 of the OC voltage (this is the output resistance).  You could decrease the resistance further (if the coupling capacitance were made large enough) to find the short circuit current.  In a model using a generic JFET, 2N3819, the resistance was 131 Ohms.

    

    This is significant because although the input impedance of the transimpedance amp is very low at low frequencies, it rises as the op amp open loop gain decreases and the loop gain  (or return ratio loop gain) decreases at high frequencies.  With a modest BW op amp (we use the TL081 with a 3 MHz GBP as compared to your OPA322 with a 10 MHz GBP) and a feedback resistance of 75k to 220k, you see a reduction in the circuit BW due to the finite Norton source resistance of 131 Ohms to below 10 kHz.  On the other hand, simulating with a wide-band op amp, say the LM6171 with a GBP = 100 MHz, there is no reduction of the BW, at least within the audio frequency band.

    Bottom line, the microphone JFET is likely to have an output resistance ~100–200 Ohms, and that is significant compared to the transimpedance amp input impedance at higher frequencies.

    Is it worth the bother?  The op amp required is higher BW (higher cost), and microphone noise (both ambient and internal) may dominate the eliminated input resistor noise.  I would probably still use the non-inverting op amp for 40 dB gain (1k and 100k say).  Now, a much smaller DC blocking capacitor can be used between the microphone and the + op amp input (with a parallel resistance to ground to determine the HP filter break frequency).  If the op amp were single supply, the offset voltage would have to be generated more precisely however.  It’s an interesting set of trade offs to consider when the microphone equivalent source has a non-zero output impedance.

    Note: in generating a Bode plot of the response where the output is divided by the input, the input voltage source is obvious to use for a Thevenin source, but the current source current must be used (not the voltage) when generating a Bode plot of the transimpedance gain (V/A).

    ECE, UT Austin

    Michael